Answer: The value of (f*g)(7) is 66.
Step-by-step explanation:
Given functions: [tex]f(x)= 4x-6\text{ and } g(x)=\sqrt{x+2}[/tex]
Since, product of two functions: [tex](u*v)(x)=u(x)\times v(x)[/tex]
[tex](f*g)(x)=f(x)\times g(x)\\\\=4x-6\times \sqrt{x+2}\\\\\Rightarrow\ (f*g)(x)=(4x-6) \sqrt{x+2}[/tex]
[tex](f*g)(7)=(4(7)-6)\sqrt{7+2}\\\\=(28-6)\sqrt{9}\\\\=22\times 3=66[/tex]
Hence, the value of (f*g)(7) is 66.
look at the image below urgent !!!!!!
Answer:
135.7 yd²
Step-by-step explanation:
Surface area of a cone: πr²+πrl, where r = radius and l = slant height
πr²+πrl
= π×3²+π×3×11.4
= 216π/5
= 135.7 yd² (rounded to the nearest tenth)
I need help with the following question
Answer:
a. 2
b. x²+10x+26
c. x²+2x+2
Step-by-step explanation:
To find each value, you plug in the x value into the function and solve.
a. 2
f(2)=(2)²-2(2)+2 [combine like terms]
f(2)=4-4+2
f(2)=2
---------------------------------------------------------------------------------------------------------
b. x²+10x+26
f(x+6)=(x+6)²-2(x+6)+2 [use FOIL method and distributive property]
f(x+6)=x²+12x+36-2x-12+2 [combine like terms]
f(x+6)=x²+10x+26
---------------------------------------------------------------------------------------------------------
c. x²+2x+2
f(-x)=(-x)²-2(-x)+2 [combine like terms]
f(-x)=x²+2x+2
Consider the graph of the quadratic function. Which
interval on the x-axis has a negative rate of change?
3
0-2 to-1
2
O -1.5 to 0
O 0 to 1
-3
-2
21
2
3
x
О 1 to 2.5
Answer:
1 to 2.5
Step-by-step explanation:
A negative rate of change requires the instantaneous slope to be negative, and the interval from 1 to 2.5 is the only place segment where that can happen.
Find the number of pieces of floor tiles each measuring 26cm long and 10cm wide needed to lay a floor measuring 260m long and 15m wide
Answer:
150,000
Step-by-step explanation:
1 m = 100 cm
260 m = 260 * 100 cm = 26000 cm
15 m = 15 * 100 cm = 1500 cm
area of floor = LW = 26000 cm * 1500 cm = 39,000,000 cm^2
area of 1 tile = 26 cm + 10 cm = 260 cm^2
number of tiles needed = 39,000,000/260 = 150,000
Answer: 150,000 tiles
WHat is the solution to the system of linear equations graphed below answers 3 1/2-4
Answer:
(3 1/2, -4)
Step-by-step explanation:
The solution is the point on the graph that the two lines intersect. The point that the lines intersect in the graph is (3 1/2, -4).
Answer:
3 1/2 , -4
Step-by-step explanation:
yes
Please help me!!Which of the following functions shows the linear parent function, Fx) = X,
shifted right?
5
F(x) = x
5
A. G(x) = x + 2
B. G(x) = 4x
C. G(x) = x - 9
D. G(x) = -x
Answer:
C. G(x) = x - 9
Step-by-step explanation:
You know that the transformation ...
g(x) = f(x -h) +k
causes parent function f(x) to be shifted right h units and up k units.
You're looking for a function that is shifted right, so you want something that looks like ...
g(x) = f(x -constant) = x - constant
Choice C has that form:
C. G(x) = x - 9
_____
A. the function is shifted up 2 units
B. the function is vertically expanded by a factor of 4 (no shift)
C. shifted right
D. the function is reflected over the y-axis (no shift)
Answer: C [G(x) = x-9]
Step-by-step explanation:
I got it right
True or False: If the data for an observation on either the dependent variable or one of the independent variables are missing at random, then the size of the random sample available from the population must be reduced, which reduces the estimator's precision and introduces a bias.
Answer:
true
Step-by-step explanation:
solve 8x=5x+3 pls pls pls
Answer:
x = 1
Step-by-step explanation:
8x = 5x + 3
Subtract 5x from both sides
8x - 5x = 5x - 5x + 3
Simplify
3x = 3
Divide both sides by 3
3x/3 = 3/3
Simplify
x = 1
Rewrite the expression as an equivalent ratio of logs using the indicated base.log17(52.875) to base 10.
Answer:
[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]
Step-by-step explanation:
Given
[tex]log_{17}(52.875)[/tex]
Required
Convert to base 10
To do this, we make use of the following logarithm laws;
[tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]
In the given parameters;
[tex]a = 52.875[/tex]
[tex]b = 17[/tex]
Substitute these values in [tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]
[tex]log_{17}52.875 = \frac{log_{10}52.875}{log_{10}17}[/tex]
Represent as a ratio
[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]
Hence;
[tex]log_{17}(52.875)[/tex] is represented as [tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]
Expression [tex]log_{17} 52.875[/tex] can be written as in form of ratio of log [tex]\frac{log_{10} 52.875}{log_{10} 17}[/tex] .
Any logarithmic expression [tex]log_{a} b[/tex] can we written as in form of ratio of log on base 10.
[tex]log_{a} b=\frac{log_{10} b}{log_{10} a}[/tex]
Here logarithmic expression is, [tex]log_{17} 52.875[/tex] comparing with above expression.
We get, [tex]b=52.875,a=17[/tex]
Substitute values of a and b in above expression.
We get, [tex]log_{17} 52.875=\frac{log_{10} 52.875}{log_{10} 17}[/tex]
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The sum of 3 times a number and 4 is 9.
Answer: x = 5/3
Step-by-step explanation:
Let the number be x
Then
3x + 4 = 9
3x = 9-4
3x = 5
x = 5/3
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Simplify the following expression.
3(2k + 3) -8k + 5 + 5
Answer:
Step-by-step explanation:
3*(2k + 3) - 8k + 5 + 5 Remove the brackets on the left
6k + 9 - 8k + 5 + 5 Combine like terms
6k-8k+9 + 5 + 5
-2k + 19
Aiko is finding the sum (4 + 5i) + (-3 + 7i). She rewrites the sum as (-3 + 7)i + (4 + 5)i. Which statement explains the
error Aiko made by using a mathematical property incorrectly
Answer:
Aiko should not have put both of the 'i' out of the brackets.
Step-by-step explanation:
As only one integer has i with it, it is not possible to take the i out of the bracket.
Find the constant of proportionality (in gallons per minute) for the second and third rows of the table. Show your work.
Answer:
16.50 gallons per minute
Step-by-step explanation:
Because this is a proportional function, we can set up the equation y = kx, where k is the constant of proportionality. By plugging in one point (and this point can be any point provided by the table), we can use the equality k = y/x to find the proportionality constant. If we plug in the information at 1 minute, we get 16.50/1 = 16.5
The constant of proportionality is same for all the rows that is 16.50 gallons per minute.
How can we calculate the Constant of proportionality?WE can calculate the Constant of proportionality as;
Constant of proportionality = no of gallons of water per 1 minute.
we have 16.50 gallons of water per 1 minute and 24.75 gallons of water in 1.5 minutes.
In 1 minute, we will have,
24.75 ÷ 1.5 = 16.50 gallons
Similarly,
33 gallons in 2 minutes. In 1 minute, we will have,
33 ÷ 2 = 16.50 gallons.
We can see that there seems to be the same constant of proportionality for the 2nd and 3rd row, that is 16.50.
Thus, a relationship between gallons of water (w) and time (t), considering the constant, 16.50, can be written as:
w = 16.50t
Hence, the constant of proportionality, 16.50, is same for all rows.
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About % of babies born with a certain ailment recover fully. A hospital is caring for babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment?
Answer:
This is a binomial experiment .
Step-by-step explanation:
As the percent is not indicated the success is the amount of percent (if given) say it is 10 % . So p will be equal to = 0.1 and q will be = 1-0.1= 0.9
and n would be five or any number as a binomial experiment is repeated for a fixed number of times.
And x would take any value of n i.e.
X= 0,1,2,3,4,5
If it is 20 % . So p will be equal to = 0.2 and q will be = 1-0.2= 0.8
The probability is the number of the percent indicated. But as it is not indicated we assume it to be 10 % or 20 % .Or suppose any number for it to be a binomial experiment.
The number of trials n would be fixed .
The success remains constant for all trials.
All trials are independent.
solve for x: 7^2x+3 =2401 . show substitution of your solution to verify the equation. show steps. show work.
Answer:
X= 1/2
Step-by-step explanation:
7^2x+3 =2401
7^(2x+3 )=2401
7^(2x+3 )= 7^4
Taking away the base because its equal to 7
Then solving the power as an equation
2x+3= 4
2x= 4-3
2x= 1
X=1/2
Now substituting x into the equation to know if we are correct
7^(2x+3 )=2401
Where x= 1/2
7^(2*(1/2) +3)= 7^4
7^(1+3)= 7^4
7^4= 7^4
7^4= 2401
Help please! Also please show the steps of how you got the answer!
30% of 40% of 15
Answer:
1.8
Step-by-step explanation:
First, find 40% of 15:
15(0.4)
= 6
Next, find 30% of this:
6(0.3)
= 1.8
So, the answer is 1.8
Find (fºg)(2) and (f+g)(2) when f(x)= 1/x and g(x) = 4x +9
[tex](f\circ g)(2)=\dfrac{1}{4\cdot2+9}=\dfrac{1}{17}\\\\(f+g)(2)=\dfrac{1}{2}+4\cdot2+9=\dfrac{1}{2}+17=\dfrac{1}{2}+\dfrac{34}{2}=\dfrac{35}{2}[/tex]
solve for x ! please help (show work)
Answer:
x = 1/2
Step-by-step explanation:
8(-2x+1) =0
Divide each side by 8
-2x+1 = 0
Add 2x to each side
-2x+1+2x = 2x
1 = 2x
Divide by 2
1/2 = 2x/2
1/2 =x
Answer:
1/2
Step-by-step explanation:
8(-2x+1)=0
Use distributive property first
-16x+8=0
Subtract 8 on both sides
-16x=-8
Divide both sides by -16 to get x by itself
x=0.5
Which is also equal to 1/2
Therefore, x is equal to 1/2
Dilate line f by a scale factor of 3 with the center of dilation at the origin to create line f'. Where are points A' and B' located after dilation, and how are lines f and f' related?
The locations of A' and B' are A' (0, 2) and B' (6, 0); lines f and f' intersect at point A.
The locations of A' and B' are A' (0, 6) and B' (2, 0); lines f and f' intersect at point B.
The locations of A' and B' are A' (0, 2) and B' (2, 0); lines f and f' are the same line.
The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
Answer:
Step-by-step explanation:
(D). The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
The location of the points A' and B' after dilation is Option(D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
What is dilation of a line segment ?The dilation of a line segment is longer or shorter in the ratio given by the scale factor. If the scale factor is greater than 1, the image of line segment will be larger than the original line, and if the scale factor is less than 1 , the image will be smaller than the original line.
How to find the coordinates of the points by dilation of given line segment ?The original line segment is given in the figure with points A and B as A(0,2) and B(2,0) .
When the line segment is dilated by a scale factor of 3, we can draw a parallel line which will be larger than the pre-image of the original line segment.
Also, the new coordinates of the points A and B will also increase by a factor of 3.
Therefore, we have A'(0,6) and B'(6,0) as the new coordinates of the line segment.
Thus, the location of the points A' and B' after dilation is Option(D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
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Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.
1. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = (x - mu )?
2. What are the units of the corresponding z scores?
A. The z scores are measured with units of "beats per minute".
B. The z scores are measured with units of "minutes per beat".
C. The z scores are measured with units of "beats."
D. The z scores are numbers without units of measurement.
Answer:
D. The z scores are numbers without units of measurement.
Step-by-step explanation:
Z-scores are without units, or are pure numbers.
Use the drawing tools to form the correct answers on the grid.
Mark the vertex and graph the axis of symmetry of the function.
fix) = (x - 2)2 - 25
Answer:
Step-by-step explanation:
Hello, this is pretty straight forward. Let me remind you the following.
The standard equation of a parabola is
[tex]y=ax^2+bx+c[/tex]
But the equation for a parabola can also be written in "vertex form":
[tex]y=a(x-h)^2+k[/tex]
In this equation, the vertex of the parabola is the point (h,k) .
So, here the vertex is the point (2, -25) and the axis of symmetry is x = 2
Thank you
Answer:
if anyone still needs the answer I added a pic
Step-by-step explanation:
Find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of -1. Show your work for full credit. Please explain the exact process of how you get your answer because I do not understand it at all. If you don't explain properly or try to just snatch some points I will try to delete your answer.
Answer:
See below.
Step-by-Step Explanation:
Please refer to the attachment.
If you have any questions, feel free to comment!
Answer:
(-1,-1)
Step-by-step explanation:
theta = -3 pi/4
Changing to degrees =
theta = -3 * 180/4 =-135
x coordinate of -1
The y value would be
= 45
tan 45 = y /1
y = tan 45
y = 1
But we are in the third coordinate so x and y are negative
The coordinates are
(-1,-1)
a sequence of transformations is described below horizontal stretch about a vertical line PQ, a translation, another horizontal stretch about PQ, a reflection over PQ.
Answer Choices:
Angle measures only
Segment lengths only
Both angle measures and segment lengths
Neither angle measures nor segments lengths
Answer:
Both angle measures and segment lengths.
Step-by-step explanation:
An angle is a shape formed by two rays that meets at a point. The angle is measured by degrees. The angle is formed by the sides of an angle which shares the common endpoint called the vertex. The line is horizontal stretch with a vertical line PQ. It will measure the angle and segments lengths.
Answer:
neither angle measures nor segment lines
help please! I need this ASAP Find the value of x
Answer:
The value of x is 30°
Step-by-step explanation:
We are given that the outer angle of the parallelogram is 60 degrees. Therefore it's respective inner angle will be 180 - 60 = 120 degrees. And, by properties of a parallelogram, the angle opposite to this angle will be 120 degrees as well.
If we draw extend the line creating angle 2x, then we will make ( 1 ) a vertical angle to 2x, ( 2 ) a 90 degree angle, and ( 3 ) and angle that we can let be y. Therefore, 2x + y = 90, and 3x + y = 120.
[tex]\begin{bmatrix}2x+y=90\\ 3x+y=120\end{bmatrix}[/tex] ,
[tex]\begin{bmatrix}6x+3y=270\\ 6x+2y=240\end{bmatrix}[/tex] ,
[tex]6x+2y=240\\-\\\underline{6x+3y=270}\\y=30[/tex],
[tex]2x + (30) = 90,\\2x = 60,\\x = 30[/tex]
Solution : x = 30°
Find the value of x in each case:
We know
Sum of two interior angles =exterior angle
[tex]\\ \sf\longmapsto 2x+x=3x[/tex]
[tex]\\ \sf\longmapsto 3x=3x[/tex]
[tex]\\ \sf\longmapsto x=1[/tex]
5 4. Cos^8A - singa^8A
Answer:[tex]z=a+bi=|z|(cos(θ)+isin(θ))tofindthtrigonometricform.√sin2(ga8A)+cos16(A)(cos(arctan(−1sin(ga8A)cos8(A)))+isin(arctan(−1sin(ga8A)cos8(A))))[/tex]
Step-by-step explanation:
An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.Beverage Sample Size Sample Mean Sample SDStrawberry Drink 10 537 22Cola 10 559 17Required:a. Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value.b. State the relevant hypotheses. c. Compute the test statistic value and find the P-value.d. State the conclusion in the problem context.e. What assumptions are necessary for your analysis?1. The distributions of compression strengths are approximately normal.2. The distributions of compression strengths have equal means. 3. The distributions of compression strengths are the same.4. The distributions of compression strengths have equal variances.
Answer:
Explained below.
Step-by-step explanation:
In this case we need to test whether the extra carbonation of cola results in a higher average compression strength.
(a)
The hypothesis for the test can be defined as follows:
H₀: The extra carbonation of cola does not results in a higher average compression strength, i.e. μ₁ - μ₂ = 0.
Hₐ: The extra carbonation of cola results in a higher average compression strength, i.e. μ₁ - μ₂ < 0.
(c)
Since the population standard deviations are not provided, we would use the t-test for difference between means.
The test statistic is:
[tex]t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}[/tex]
[tex]=\frac{537-559}{\sqrt{\frac{22^{2}}{10}+\frac{17^{2}}{10}}}\\\\=\frac{-22}{8.792}\\\\=-2.502[/tex]
The test statistic value is -2.502.
(c)
Compute the p-value as follows:
[tex]p-value=P(t_{16}<-2.052)=0.012[/tex]
*Use a t-table.
The p-value of the test is 0.012.
(d)
The significance level of the test is, c
p-value = 0.012 < α = 0.05.
The null hypothesis will be rejected.
Conclusion:
The data suggest that the extra carbonation of cola results in a higher average compression strength.
(e)
The assumption necessary for the analysis is:
The distributions of compression strengths are approximately normal.
The correct option is (A).
solve the equation[tex]x^3+\left(y^'\right)^3-3xy^'\:=0[/tex]
Answer:0
Step-by-step explanation:
3x=3xy
x=0
y=0
3 times 0 = 0
If 2 = 5, what is 2 3 − 4?
Answer:
27.5
Step-by-step explanation:
3 = 7.5
4 = 10
5*7.5=37.5-10=27.5
Seriously. 2=5 contradicts.
An object is moving at a speed of 5 kilometers every 4.5 hours. Express this speed in miles per minute
Answer:
Step-by-step explanation:
1 km = 0.621 mi
1 hr = 60 min
(5 km)/(4.5 hr) × (0.621 mi)/km × (1 hr)/(60 min) = (0.0115 mi)/min